As an essential component of real-time system design, priority is utilized to resolve conflicts in resource sharing and design for safety. For real-time systems that introduce priorities, each task is assigned a priority, which leads to the possibility of low-priority tasks being preempted by high-priority tasks at runtime, thus creating a preemptive scheduling problem for real-time systems. Existing research on this problem lacks a modeling and automatic verification method that can visually represent the priority of tasks and the dependencies between tasks. To this end, a preemptive priority timed automata (PPTA) is proposed and a preemptive priority timed automata network (PPTAN) is introduced. First, the priority of a task is represented by adding the priority of migration to the timed automata, and then the migration is adopted to correlate tasks with dependencies so that PPTA can be applied to model real-time tasks with priority. The blocking position is also added to the timed automata, so PPTAN can be used to model the priority preemptive scheduling problem. Second, a model-based transformation method is proposed to map the PPTA to the automatic verification tool UPPAAL. Finally, by modeling an example of a multi-core multi-task real-time system and comparing it with other models, it is shown that this model is not only suitable for modeling the priority preemptive scheduling problem but also for accurately verifying and analyzing it.